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Math Methods Midterm A
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Terms in this set (27)
Conceptual Understanding
comprehension of mathematical concepts, operations, and relations
Teaching Math in Real-World Contexts
Helpful to motivate students and access prior knowledge; Should not be elevated to a general principal; some math must be taught for math's sake alone; students should be able to say "this learning will help me do this"
Five NCTM Content Standards
Number and Operations; Measurement; Geometry; Algebra; Data Analysis and Probability
Five NCTM Process Standards
Problem Solving; Reasoning and Proof; Communication; Connections; Representation
Reasoning
the logical thinking that helps us decide if our answers make sense
Proof
Additional evidence for that
Communication
Points the importance to be able to talk about, write about and explain math ideas
Connections
ex. Fractions, percents, decimals; curriculum integration (having a theme that goes through many topics)
Representation
Math should be connected to the real world
Number Sense
understanding and reasoning about numbers (gradual)
3 Ways Children Learn Number Sense
Naturalistic Opportunities; Informal Learning; Structured Learning Experiences
Informal Learning of Mathematics
Provide play materials that foster math content; Occurs when a comment or question is posed to the child that expands on prior knowledge during naturalistic activities
Dixi (star)
Concrete (manipulatives); Representational or semiconcrete (Drawing a picture); Abstract
Cardinality
Last number said+ amount/ age 4.5 to 5 years
Counting Sequence
Rote memorization
Counting down
calls for reverse thinking and is more common in the early grades
Ordinal numbers
The relative position of the number (first, second)
Metacognition
children must be encouraged to think about their own learning
Heuristics
solving problems
Knowledge of problem solving strategies
Heuristics ( Polya's 4 step process)
1. teaching problem solving
2. Devise a plan
3. Carry out the plan
4. Look back (most important) evaluate solution
Patterns =
fundamental skill for algebraic thinking
Generalizing patterns is
KEY
TEK Required Patterns
Repeating Patterns
Growing Patterns
Repeating Patterns
EC focused
very common
aab, or ab ab
Growing patterns
More complicated
One value or antoher
foundational to the study of functions
Doing and Un-Doing
ability to undo and do math (work backwards)
Building Rules to represent Functions
ability to recognize patterns and organize data (input related to output)
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